[Pw_forum] Monolayer MoS2 band Structure

[Cameron Foss]

Hello,

I am attempting to obtain the band structure of monolayer MoS2, however my
results so far do not agree well with what has been documented for
monolayer (ML) MoS2. I consistently get an indirect band gap for ML MoS2
caused by the 'Q-valley' minimum seen in bulk MoS2.

I have tested the code with interplanar distances of 15 and 30 angstroms to
eliminate any interplanar interactions. There have been several papers that
report the band structure for ML MoS2 from first principles, they have used
functionals from LDA, GGA, and an HSE hybrid functional. My best success
has been with GGA-PW91(see input file below). Note in all my simulations I
have measured a band gap of ~1.9eV which is in agreement with reported
values.

I am uncertain as to what the issue could be? I have tested 3 different
PPs.

%%%%%%%%%%%%%%%%%%%%
Details on simulations:

 Specifically, my simulations continue to show that the 'Q-valley' is
slightly lower (16meV~30meV) than the minimum at the K point, suggesting an
indirect band gap. However ML mos2 has been widely shown to have a direct
band gap at the K point where this 'Q-valley' along the conduction band is
suppressed above the K-point minimum.

I run a scf (pw.x) calculation first, followed by an nscf (pw.x) run, and a
bands calculation with pw.x (and of course bands.x to retrieve the energy
values). I specify 16 bands for nbnd, kpoints along symmetry paths, and a
MP grid of 8x8x1 with a 1 1 1 offset.

Input file:

&control
    calculation='scf'                      !nscf, then bands
    restart_mode='from_scratch',
    !pseudo_dir='directory where pseudopotentials are stored/',
    !outdir='directory where large files are written/'
    pseudo_dir='/home/cameron/QE/espresso-5.1/pseudo/',
    outdir='/home/cameron/QE/espresso-5.1/2dout'
    prefix='mos2-gga',
 /
 &system
    ibrav=4, celldm(1)=5.8364, celldm(3)=10,
    nat=3, ntyp=2, ecutwfc =70, ecutrho=300         ! specified nbnd=16
 /
 &electrons
    conv_thr =  1.0d-15                   ! reduced to 1.0d--12 for nscf,
bands
    mixing_beta = 0.5                     ! increased to 0.7 for nscf, bands
 /
ATOMIC_SPECIES
 Mo  95.94    Mo.pw91-n-van.UPF
 S   32.065   S.pw91-n-mt.UPF
ATOMIC_POSITIONS bohr
S        0.00002  -0.00001   0.000000000
Mo       2.91822   1.68481   2.929886569
S        0.00002  -0.00001   5.859870374
K_POINTS automatic
 8 8 1 1 1 1

I ran into some convergence issues with all the bands with this conv_thr in
the nscf and bands calculations, so i had to reduce it to 1.0d-12 for those
calculations. I also used a mixing beta of 0.7 for both the nscf and bands
calculations. I am uncertain as to whether changing mixing_beta's between
calculations is of importance or not as well, but I do not think this is
the case.

Best regards,
Cameron
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